The given equation is
[tex]y=3x-9[/tex]The new line is perpendicular to the given equation, which means we have to use the following formula.
[tex]m\cdot m_1=-1[/tex]Where the slope of the given line is 3 (the coefficient of x).
[tex]m\cdot3=-1[/tex]We solve for m.
[tex]m=-\frac{1}{3}[/tex]So, the slope of the new perpendicular line is -1/3.
According to the problem, the y-intercept of the new perpendicular line is 4. Now, we use the slope-intercept form to write the equation.
[tex]\begin{gathered} y=mx+b \\ y=-\frac{1}{3}x+4 \end{gathered}[/tex]